This thesis investigates stability limits in inverter-dominated AC grids and how GFM converters can mitigate weaknesses introduced by GFL control. Building on small-signal and impedance-based frameworks, the work first develops dq-admittance models for GFL and GFM inverters and a closed-loop formulation that couples converter and network dynamics. Using graph-theoretic network modelling (grounded Laplacian and Kron reduction), the study integrates generalised short-circuit ratio (gSCR) as a strength metric for multi-infeed systems.

Four case studies validate the framework: a single GFL on an infinite bus, a single GFM, a parallel GFL–GFM pair, and a multi-IBR network. For the single-converter cases, eigenvalue analysis shows the PLL-synchronisation vulnerability of GFL units under weak grids and the instabilities induced in GFM inverters under string grids, proving their duality. The voltage-source behaviour of GFMs is then utilised and used to estimate the minimum GFM penetration needed to stabilise GFLs in weak grid conditions. In multi-IBR settings, gSCR extends SCR to characterise the strength of the whole network. Combined with GFM impedance modelling, it guides the placement of GFM inverters to increase system strength.

The thesis proposes a practical workflow for improving stability in weak multi-IBR networks: identify the critical SCR of representative GFLs via small-signal analysis; compute bus-wise gSCR on the reduced network; assess margins using local single-IBR loop checks; and, by modelling GFMs as voltage sources behind frequency-dependent impedances, select locations/capacities that maximise strength at critical buses. Results show that (i) there exists a critical strength threshold for GFL stability, and adding GFMs raises the effective strength in line with the GFL–GFM duality; (ii) the voltage-source-plus-impedance model predicts how much strengthening GFMs provide; and (iii) while these tools give reliable stability indications, component limits (voltage/current) can still be violated under severe weakness and must be verified in time-domain simulations.